For long range detection with low duty cycles, like ABMD, the power per pulse is quite important. That's one domain where vacuum tube powered ESAs still have an edge over solid state powered ESAs. That might explain why the US Navy decided not to replace the SPY-1D with AESA until high power GaN antennas matured.
Actually they tried, with the SPY-3 and SPY-4 radars, intended for a new generation of warships, the CG(X) and the DD(X), Zumwalt, Ford class. Then they ran into issues, including both the radars. Then the quick advent of GaN made both radars obsolete. One has to consider the long list of advantages an AESA has, over one potential advantage that a PESA might have. If you look at many of these long range OTH stealth detecting radars, they are UHF and VHF AESAs. And not just that, but also radars used on AEW aircraft.
High power per pulse is just a great way to be detected by ESM, also known as passive or covert radars, which can even obtain your ship's position to allow for a long range OTH antiship missile attack. You have to prefer detection using the lowest possible power to allow for LPI, or to make your own radar less detectable. Hence sensitivity is really what you are after with GaN.
With an AESA, you can modulate the waveform to "peak" and create a similar phenomenon as a high power pulse. Furthermore, the agility of AESA can make the waveform look pseudo random that it can be construed as static, and not trigger off threat ESM.
Range determines the length of your duty cycle, since you have to wait for the echo before you can transmit again, which is determined by the time it takes to travel by the speed of light / 2, and no less. So for long range you cannot have short PRF anyway, and short PRF will not allow for long range.
Another thing that favors AESAs is that they work with pulse doppler techniques. With PESA, the shifters have to be reset after each transmission and that somehow affects creates noise that affects the use of pulse doppler techniques. That is why for so long, fighter jets use slotted array antennas, that these radars become synonymous with Pulse Doppler, and which is why, it is preferable to bypass PESA and straight into AESA for the next generation of fighter radars. For PESA you would have to use MTD to detect moving targets.
Then because of the central transmitter, only two of the four array faces can be used to beam simultaneously (from the sources you quoted). In contrast the AESA can light up all four faces, even have different frequencies among them, or even across the face. With a PESA, all the four arrays will have to be of the same frequency and pulse.
One thing for sure about the wiki articles, is that the Type 346 arrays would have to use S-band due to their size. If you were to using C-band elements, the number of elements needed to cover such an area may hit over 10,000, far more than the SPY-1's 4500 elements or the MPQ-53's over 5,000. And each of those C-band elements are AESA. You are going to run into issues with the sheer cost of each array and how you can cool those things.
